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A very robust and inexpensive kinetic assay for determining rates of hydrolysis of p-nitrophenyl phosphate by the enzyme alkaline phosphatase is presented. The reaction increases in rate with increase in pH. The enzyme is competitively inhibited by the reaction products, uncompetitively inhibited by L-phenylalanine, and responds to the presence of two cofactors, magnesium and zinc ions. The reaction rate increases as Mg2+ concentration is increased from 1–5 mM. With increasing Zn2+ concentration, the reaction rate is stimulated and then depressed. Experimental work on the interaction between Mg2+ and Zn2+ in the reaction is suggested for more capable students.
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Experience has shown that enzyme assays used to teach introductory enzyme kinetics should ideally meet a number of criteria. (i) The assay should be reliable and show a prolonged linear rate of reaction to maximize the possibility that inexperienced students will obtain satisfactory data; (ii) given the funding situation at most institutions, the reagents should be inexpensive; and (iii) if preparation time is limited because multiple laboratory classes are offered throughout the week, reagents should be stable. For 2 years we have successfully used variants of one such kinetic assay as the basis for teaching enzyme kinetics in a 2nd-year undergraduate laboratory class. The assay presented in this article involves the hydrolysis of p-nitrophenyl phosphate by a commercially available preparation of the enzyme alkaline phosphatase.
A number of publications describe class experiments with acid phosphatase [1–4], which is easily prepared by aqueous extraction of wheat germ and which can be colorimetrically assayed. However, these enzymatic studies all involve a fixed-time assay where a single measurement of product concentration is made after stopping the reaction following a given period of time. Fixed-time assays can be time-consuming because a basic assumption in the Michaelis-Menten approach to enzyme kinetics is that the enzyme is substrate-saturated. Consequently, initial velocities must be determined from reaction data that are linear with respect to the decline in substrate concentration (or increase in product concentration) over time. In fixed-time assays considerable effort is required to establish the duration in which the reaction between enzyme and substrate is linear. Moreover, the validity of the linear relationship must be confirmed each time that the reaction mixture is changed to accommodate the study of, for example, enzyme inhibitors or cofactors. Conversely, if one uses a kinetic assay, in which the reaction is continuously monitored, each data set reveals how long the reaction is linear, and any deviations from linearity are readily apparent. It is not possible to run a kinetic assay with acid phosphatase using p-nitrophenyl phosphate as substrate because the product, p-nitrophenol, is colorless at acidic pH. I consequently suggest that if the actual enzyme to be used is not critical, alkaline phosphatase be used instead of acid phosphatase. Alkaline phosphatase is inexpensive, is very stable, and shows interesting responses to millimolar concentrations of magnesium and zinc ions both separately and together. For enzyme inhibition studies, alkaline phosphatase is competitively inhibited by both of its reaction products and is uncompetitively inhibited by the L-isomer of the amino acid phenylalanine.
The experimental work described here was developed for, and tested in, a 2nd-year undergraduate laboratory course designed primarily to provide students with laboratory experience. However, enzyme assays are so widely used that the work with alkaline phosphatase would be an appropriate component of a laboratory class associated with an introductory course in biochemistry or cell biology.
A BRIEF INTRODUCTION TO THE PHOSPHATASES
Phosphatases are enzymes that catalyze the hydrolysis of esters of phosphoric acid. They occur in the cells and extracellular fluids of a wide range of organisms. This large and complex group of enzymes falls into four general types based on the chemical nature of the substrate or the type of hydrolytic reaction that is catalyzed. One group, the phosphomonoesterases, hydrolyzes monoesters of phosphoric acid such as α-glycerophosphate or glucose 6-phosphate. Some phosphomonoesterases are highly substrate-specific. For example, in gluconeogenesis, fructose-1,6-bisphosphatase specifically converts fructose 1,6-bisphosphate to fructose 6-phosphate and inorganic phosphate. Other phosphomonoesterases react with a broad range of substrates, which share common structural motifs. The phosphomonoesterases that lack substrate specificity are classified as acid or alkaline phosphatases based on their pH optima. Acid phosphatases function best at around pH 5.0 and are inhibited by fluoride ion but not by divalent cation-chelating agents. The alkaline phosphatases have pH optima of about 9.0 and are not generally sensitive to fluoride ion but are inhibited by divalent cation-chelating agents like EDTA (ethylene diamine tetraacetic acid, disodium salt).
Students prepare reaction mixtures and solutions for standard curves from the following previously prepared stock solutions.
Enzyme: bovine and calf intestinal alkaline phosphatase (phosphoric monoester phosphohydrolase (alkaline optimum), EC 126.96.36.199) (Sigma) diluted 1:10,000 with reaction buffer containing 1 mg/ml bovine serum albumin (Sigma).
Substrate: Sigma 104 phosphatase substrate (p-nitrophenyl phosphate, disodium, hexahydrate), 1.35 mM (0.5 mg/ml) in reaction buffer.
Product: p-nitrophenol (Sigma), 1 mM in reaction buffer.
Reaction buffer: Tris-HCl buffer (see figure legends for concentrations and pH) with or without 5 mM MgCl2·6H20.
Enzyme inhibitors: 25 mM monobasic sodium phosphate (NaH2P04·H20), 0.5 mMp-nitrophenol, 50 mM L-phenylalanine (Sigma). All were dissolved in reaction buffer at the concentrations and pH values given in the figure legends.
The Basic Assay
Alkaline phosphatase hydrolyzes the colorless, synthetic substrate p-nitrophenyl phosphate to produce a yellow-colored product, p-nitrophenol and inorganic phosphate: Reaction 1
The initial velocity (vo) of the reaction, in micromoles of product produced/minute, can be calculated from the increase in absorbance at 400 nm (ΔA400) measured at timed intervals during the reaction.
Typical reaction mixtures to which the enzyme is added are shown in Table I. These mixtures provide a satisfactory concentration range for making a Lineweaver-Burk plot. In reactions involving the addition of inhibitors or cofactors dissolved in reaction buffer the volume of reaction buffer is reduced to give a total volume of 5 ml. The volume of enzyme preparation added to start the reaction is one that will generate a ΔA400 of ∼0.3–0.4 in the tube with the highest substrate concentration during the time that the reaction is monitored.
To analyze the rate data, a standard curve of A400 against p-nitrophenol concentration is needed. The linear relationship between absorbance and p-nitrophenol concentration holds up to a concentration of about 40 μM. If reaction buffers of different pH values are used, a separate standard curve must be made using reaction buffer at each pH. As with many colored compounds, the absorbance of p-nitrophenol is pH-sensitive.
Use the reaction mixture without enzyme to adjust the needle on the spectrophotometer meter to zero absorbance. Add a volume of enzyme preparation (typically 20 μl). Cover the tube with Parafilm, invert three times (do not shake) to mix the contents, and return the tube to the spectrophotometer. The absorbance value will be increasing. When the absorbance reaches a convenient value (e.g. 0.010 or 0.020), start timing. Record absorbance values at 30-s intervals for 3 min. (Assays can be run for longer periods if high concentrations of enzyme inhibitors are present).
Graph the change in absorbance (ΔA400) against time to ensure that the reaction is linear over the time that the reaction is monitored. An important assumption in the derivation of the Michaelis-Menten equation is that the concentration of the enzyme-substrate complex ([ES]) instantly reaches a steady state and remains unchanged during initial velocity measurements. In this assay, this presents no problem as the linear relationship between the increase in absorbance and time holds for at least 7 min (Fig. 1), twice the duration of the assay. This prolonged linear phase is particularly useful when measuring reaction rates in the presence of high enzyme inhibitor concentrations.
Determine the ΔA400/minute for the initial linear part of the reaction.
The ΔA400/minute corresponds to an increase in the concentration of the product, p-nitrophenol, per minute (Δc/minute) and an equal decrease in the concentration of the substrate. The corresponding Δc/minute can be determined by: (i) interpolation of the standard curve or (ii) using the absorption coefficient (ϵ) for p-nitrophenol derived from the slope of the standard curve. If the x axis of the standard curve is expressed in moles/liter then:
where A = absorbance, c = concentration in moles/liter, and ϵ = liters/mole/centimeter. Therefore
To find the number of moles of p-nitrophenol produced per minute, correct for the total volume of the reaction mixture; e.g. if 20 μl of enzyme preparation are added to 5 ml of buffered substrate (total volume = 5.02 ml) then
Convert this value to micromoles/minute = initial velocity (vo).
Vmax, the maximum initial velocity (or limiting velocity), and Km, the Michaelis constant, which is defined as the substrate concentration that produces an initial velocity equal to one-half of Vmax, can be determined from a double reciprocal (Lineweaver-Burk) plot. The reciprocal of the substrate concentration (1/[S]) on the x axis is plotted against the reciprocal of vo on the y axis. A straight line is fitted through the points and extrapolated through the y axis and the negative side of the x axis. The intercept on the y axis = 1/Vmax, and the intercept of the x axis = −1/Km. (The Lineweaver-Burk plot has been justifiably criticized as a means for determining Km and Vmax [5, 6]. However, it is a useful starting point for students being introduced to enzyme kinetics.)
RESULTS AND DISCUSSION
Stability of the Enzyme and Buffered Substrate Preparation
To demonstrate that enzymes only catalyze reactions that proceed slowly in their absence it is instructive to leave a tube of buffered substrate in the lab between classes. This shows that the substrate is slowly converted to product at room temperature in the absence of enzyme. A 5.0-ml solution of 0.54 mMp-nitrophenyl phosphate in buffer at pH 9.0 increased in A400 by 0.013 each day over a 3-day period. This is ∼15,000 times slower than the rate of conversion of substrate to product in the presence of 20 μl of our enzyme preparation.
At lower temperatures, both the buffered substrate solution and the diluted enzyme preparation are remarkably stable. To check for long term stability, substrate solution and enzyme preparation were stored at −8 °C for 3 months. At the end of this time, the rate of hydrolysis of substrate by the enzyme was still 70% of that using freshly prepared solutions.
Effect of pH on the Reaction
As its name indicates, alkaline phosphatase is highly pH-sensitive. In the effective buffering range for Tris-HCl, the initial velocity of the hydrolysis of substrate by alkaline phosphatase increases more than 6-fold from pH 7.0 to pH 9.0 (Fig. 2). Furthermore, the values Km and Vmax are clearly affected by pH (Fig. 3). For further information on the effect of pH on enzyme-catalyzed reactions see Refs. 7 and 8 for reviews.
Inorganic phosphate (Pi) and p-nitrophenol, the products of the hydrolysis of p-nitrophenyl phosphate by alkaline phosphatase, both competitively inhibit the enzyme. A Lineweaver-Burk plot for the reactions, in 1 M Tris buffer (pH 8.0) containing 5 mM Mg2+ in the presence and absence of 30 μMp-nitrophenol, shows that the Vmax remains the same but that the Km is increased from 0.1 to 0.125 mM in the presence of the inhibitor (Fig. 4). Similarly, a Lineweaver-Burk plot for the reactions, in 0.5 M Tris buffer (pH 9.0) containing 5 mM Mg2+ in the presence and absence of 0.1 mM monobasic sodium phosphate (Pi), shows that the Vmax is the same and that the Km is increased from 0.2 to 0.5 mM(Fig. 5).
Lineweaver-Burk plots that show the same Vmax but increased Km in the presence of the inhibitor are characteristic of competitive inhibition. In competitive inhibition, the inhibitory molecule is thought to bind reversibly at the substrate-binding site on the enzyme consequently preventing the substrate from binding. Since both Pi and p-nitrophenol appear to bind at the active site on the enzyme we might reasonably deduce that the substrate-binding site on the enzyme recognizes both the phosphate group and some other part of the p-nitrophenyl phosphate molecule when forming the enzyme-substrate complex.
Examples of uncompetitive inhibition in enzyme reactions that involve a single substrate are rare. In uncompetitive inhibition, the inhibitory molecule is thought to bind to the enzyme-substrate complex but not to the free enzyme. The inhibited ES complex is non-functional so the Vmax decreases when the inhibitor is present. When the inhibitor is present, the Km value also declines because the reduced number of uninhibited ES complexes require a lower substrate concentration to half-saturate the enzyme. Consequently, in a Lineweaver-Burk plot, the inhibited slope is parallel to, and shifted to the left of, the uninhibited slope. The L-isomer of the amino acid phenylalanine at 5 mM is an uncompetitive inhibitor of alkaline phosphatase (Fig. 6). Interestingly, the D-isomer of phenylalanine is not an inhibitor . This fact should permit an investigation of steric specificity in the uncompetitive inhibition of alkaline phosphatase by phenylalanine.
Magnesium and Zinc Ions Are Cofactors of Alkaline Phosphatase
Some enzymes are catalytically active without a requirement for additional ions or molecules. In others, activity depends on the presence of a non-protein cofactor. Cofactors fall into two major groups; they are either metal ions or organic compounds. A familiar example of the latter group is flavin-adenine dinucleotide (FAD). Intestinal alkaline phosphatase uses Mg2+ and Zn2+ ions as cofactors. Alkaline phosphatase is a glycoprotein with a molecular weight of ∼140,000. It is a dimer of two very similar or identical subunits. Each subunit (∼69,000 molecular weight) contains a tightly bound zinc atom that contributes to the structural integrity of the polypeptide and a less tightly bound zinc atom that is required for catalysis. Each subunit also contains a different binding site for Mg2+ ions that stimulate enzymatic activity [10, 11]. If magnesium is omitted from the reaction mixture, both Km and Vmax are reduced. Typical values for Km and Vmax are ∼0.25 and ∼0.1 mM and ∼0.03 and ∼0.01 μmol of product/min, respectively, in the presence and absence of 5 mM magnesium chloride. The reaction rate is clearly enhanced in the presence of additional Mg2+ ion. However, it should not be assumed that no Mg2+ or Zn2+ ions are present when the reaction mixture is not supplemented with these ions. The Sigma alkaline phosphatase preparation contains 1 mM Mg2+ and 0.1 mM Zn2+ so that diluted enzyme preparations would be expected to carry some bound Mg2+ and Zn2+.
In the descriptions of the effects of adding Mg2+ and Zn2+ ions to the reaction mixtures that follow it should be emphasized that the concentrations of these ions are nominal. It is difficult to make small volumes of dilute solutions accurately, and both magnesium chloride and zinc chloride are extremely hygroscopic. Even when stored in a vacuum desiccator, the stock chemicals absorb water. As a consequence, we are unable to make solutions of known concentration by dissolving a given weight of reagent in a known volume of solvent. As a result, there can be considerable variation in the magnitude of the response at the reported ion concentrations. Fortunately, the trend of the response to increasing ion concentration is consistent.
A dramatic example of the effect of magnesium concentration is shown in Fig. 7. The initial velocity of the reaction more than doubles as the Mg2+ concentration is increased up to the nominal value of 5 mM. In some other cases, the effect of Mg2+ concentration has been less pronounced, probably because of the difficulty of producing stock solutions of precisely known concentration.
The effects of different concentrations of zinc are more complex. Low concentrations (∼0.5–1.0 mM) produce a slight stimulation in the initial velocity, whereas concentrations above 3.0 mM are inhibitory (Fig. 8). The explanation for this response involves a competitive interaction between magnesium and zinc ions. There is a binding site for magnesium on each enzyme subunit, and when Mg2+ is bound the activity of the enzyme increases. Each subunit also contains a separate zinc-binding site that is saturated at low concentrations. Zinc binding also enhances the catalytic activity of the enzyme. However, at higher zinc concentrations, zinc ions bind to the magnesium-binding site with a higher affinity. This displacement of Mg2+ by Zn2+ results in the loss of the magnesium-enhanced activity . A sample experiment using different Mg2+ and Zn2+ concentrations, both separately and together, illustrates this phenomenon. Fig. 9 shows that 1 mM Mg2+ approximately doubles the initial velocity of the reaction, which is also somewhat enhanced by 1 and 2 mM Zn2+. At 3 mM, zinc ions become inhibitory, reducing activity to 93.9% of the control value. The inhibitory effect of 3 mM Zn2+ is reduced to 97.4% of the control value in the presence of 1 mM Mg2+.
Do in Vitro Studies on Enzyme Kinetics Inform Us about How Enzymes Function in Vivo?
Like most instructors, I try to find relevance in the lab work that I offer to students. However, we should be skeptical about any conclusions drawn about the behavior of alkaline phosphatase, in the intracellular or extracellular environment, from the type of studies described in this article. Many of the reaction components and conditions are not found in nature. As examples, (a) the substrate, p-nitrophenyl phosphate, is synthetic, (b) the buffer contains Tris, which is also synthetic, (c) Tris stimulates the activity of alkaline phosphatase in a concentration-dependent manner , (d) the molar and ionic concentrations of the reaction mixtures are unphysiological, (e) the pH used may or may not reflect that occurring in vivo, and (f) the temperature is ∼12 °C too low for a mammalian enzyme.
Moreover, the uncritically repeated explanations for kinetic phenomena “written by people more interested in molecular biology than in kinetics who think that nothing has been learned…. since 1934”  are frequently oversimplified or unsupported. Examples include: (a) the suggestion that the Km value gives an indication of the degree of affinity of the enzyme for its substrate (it may or may not), (b) the perfectly logical suggestion that the Km value gives an indication of the substrate concentration that the enzyme would encounter in vivo (largely unsupported), and (c) the suggestion that changes to Km and Vmax in the presence of inhibitors can tell us about the mechanism of inhibition. It has been argued  that terms like competitive and uncompetitive inhibition should be “operational” in that they only describe the observations. (These authors avoid any discussion of noncompetitive inhibition!)
I do not intend to suggest that enzyme kinetic studies have no value in undergraduate education. As long as we do not overinterpret the results and emphasize that kinetic studies “in conjunction with other techniques”  can provide useful insights into the mechanisms of enzyme action, studies of this type are a valuable introduction to the design and execution of laboratory experiments.
The kinetic assays using alkaline phosphatase described in this article have been performed successfully by a large number of 2nd-year undergraduates over a 2-year period. The assay is completely reliable and shows a prolonged linear reaction rate with no lag phase. The latter property is particularly useful for inexperienced students, who tend to procrastinate before taking the first absorbance reading and also permits reactions to be run for longer periods as necessary in the presence of high concentration of enzyme inhibitors. The reagents are inexpensive; a 30-μl sample of the enzyme as purchased from Sigma is more than enough for over 600 students working in groups of three to four students to run assays for 13 weeks in a year. Similarly, 5 g of substrate exceeds the requirements for the same numbers. The great stability of the reagents allows us to make up batches large enough for 2 or more weeks of classes and store them at −8 °C in appropriately sized aliquots. Moreover, for the reasons outlined in the Introduction, kinetic assays are superior to fixed-time assays because the rate of reaction can be continuously monitored. These assays can also be performed very rapidly. As an example, Fig. 6 contains data points from only 10 reactions. Ten such reactions and the data analysis fit comfortably into the usual duration of a laboratory class.
Before working on kinetic assays our students spend three laboratory classes gaining experience in spectrophotometry and, equally importantly, pipetting technique. After this, the majority of students can manage most of the experimental work described.
An exception is the work involving different concentrations of zinc ions where differences between controls and treated values are often too subtle to be detected by less experienced hands. The work with zinc is consequently better suited to upper level undergraduates. However, if more able students can be identified in advance, they can be offered the opportunity to investigate zinc and magnesium ions as cofactors, while the remainder of the class works with only magnesium.
Finally, student comprehension of the preceding work is greatly enhanced if they are assigned readings on enzyme kinetics, enzyme inhibition, and cofactors from one of the many excellent biochemistry laboratory books [13–15] or standard course texts [16–20] before attending class.
Table Table I. Typical reaction mixtures and the resulting substrate concentrations
1.35 mMp-nitrophenyl phosphate in reaction buffer
Resulting substrate concentration
I am grateful to Fawzi Razem, who prepared the figures, and to Professor Mark Bernards for helpful comments on a draft of the manuscript.